Problem: Simplify the following expression: ${7(1+2p)-3(3p+10)}$
Explanation: Distribute the ${7}$ into the first set of parentheses: $ {7(}\gray{1+2p}{)} - 3(3p+10) $ $ {7+14p} - 3(3p+10) $ Distribute the ${-3}$ into the parentheses: $ 7+14p {-3(}\gray{3p+10}{)} $ $ 7+14p {-9p-30} $ Rewrite the expression to group the ${p}$ terms and numeric terms: $ {14p - 9p} + {7 - 30}$ Combine the ${p}$ terms: $ {5p} + {7 - 30}$ Combine the numeric terms: $ {5p} {-23}$ The simplified expression is $5p-23$